Blitz the courgette in a food processor, and then mix in the yoghurt, coconut oil, eggs, vanilla extract, lime zest and juice, and 45g pistachios.
Fold in the flour and baking powder, then pour mixture into a pudding basin.
Cook in the microwave on full power for between 5 -15 minutes depending on your microwave. You should take it out every five minutes, and pierce it with a skewer to check if it is done. If cake mix is on the skewer put it back in the microwave.
Take out of the basin and allow the cake to cool.
Beat together the butter and cream cheese, while gradually adding icing sugar.
Pour the buttercream over the cake and spread all over. (you will have a lot of buttercream left over, which you can freeze and save for another cake).